In the parallelogram BCDE, the bisector of angle C intersects the side DE at point K with EK = 7
| February 1, 2021 | education
In the parallelogram BCDE, the bisector of angle C intersects the side DE at point K with EK = 7 cm DK = 12 cm find the perimeter of the parallelogram.
Consider the parallelogram BCDE.
Since the CK is the bisector of the angle BCD and the lines BC and DE are parallel, the angles KCB and CKD are crosswise. We have:
DCK = KCB = CKD.
Therefore, triangle CDK is isosceles:
CD = DK = 12 cm.
We also have:
DE = EK + DK = 7 + 12 = 19.
Thus, the perimeter P of the parallelogram BCDE is:
P = BC + CD + DE + BE = 2 * (CD + DE) = 2 * (12 + 19) = 62.
Answer: 62 cm.
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